Stokes Law, also known as Stokes’ Law, is a law of physics that describes the motion of small, rigid spheres through a fluid medium. It was derived by George Stokes in the 19th century and is named after him.
It deals with the drag force that acts when a solid sphere moves through a fluid at low Reynolds number. The formula that embodies Stokes’ Law equation is as follows: F = 6πηrv, where F is the total drag force on the sphere, η is the fluid viscosity and r and v are the radius and velocity of the sphere, respectively.
In essence, Stokes’ Law states that the drag force on a small moving object is directly proportional to the viscosity of the fluid, the radius of the sphere, and the velocity of the object.
What is the Stokes law explain?
Stokes law states that the downward acceleration of a falling spherical object in a force field (such as a gravitational field) is proportional to the radius of the object. The law is often used to calculate the terminal velocity of a falling object, or the velocity at which the force of gravity equals the resistive drag force of an object’s motion through a fluid.
It is a special case of Newton’s second law of motion that explains the motion of objects falling in a viscous fluid, such as air or water. The law was formulated by George Gabriel Stokes in 1851, who found it to be a good approximation for the motion of small, negatively buoyant solid particles when their diameter is less than 1-2 mm.
The law is named in his honor.
In a mathematical form, Stokes Law states that the force F (drag force) is equal to the product of the coefficient of viscosity (μ) of the medium, the velocity V of the sphere and its radius R:
F = 6πμVR
In this form, F is the viscous resistance force or drag, μ is the viscosity of the medium, V is the velocity of the spherical body, and R is the radius of the sphere. Thus, Stokes Law states the drag force is proportional to the magnitude of the velocity, and to the radius of the sphere.
This equation only applies to spheres because the drag force on a non-spherical object is much harder to calculate.
What is stock’s force Class 11?
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Which of the following formula states the Stokes law?
The Stokes law is an equation used to calculate the frictional force experienced by an object as it moves through a fluid medium. It is expressed as:
Fd = -6πηrv,
where Fd is the frictional force, η is the viscosity of the fluid, r is the radius of the object, and v is its velocity. The Stokes law is a result of the assumptions of laminar flow, which states that a fluid medium can be considered as a collection of layers that slowly shear one another.
In its simplest form, the equation states that the frictional force between the object and the fluid layers is proportional to the velocity with which the object moves through the fluid. Thus, an object moving faster through a fluid will experience a larger frictional force than one moving slowly.
What is Stokes method physics?
Stokes method physics is a mathematical tool that can be used to solve problems related to heat transfer in fluids. It is based on the assumption that the viscosity of a fluid can be described as a linear function of temperature.
This allows for the calculation of temperatures, pressures and other properties of fluids based on Stokes’ equations. Stokes method is used to determine the frictional force or drag that a fluid exerts on a solid surface or body, as well as to calculate various aspects of convective heat transfer.
The method is particularly useful for solving problems involving viscous fluids, such as aero, hydrodynamic and thermal problems. The basic thing that makes Stokes method particularly useful is its linearity, allowing for the calculation of exact solutions.
Examples of applications include the calculation of velocity distribution and temperature fields within a laminar boundary layer, or the analysis of a cooling process in a system with combined convective and thermal effects.
What is the dimension of Stokes law?
Stokes’ law is expressed mathematically as F = 6πηrv, where F is the force of drag, η is the dynamic viscosity of a fluid, r is the radius of a spherical object, and v is the velocity of the sphere relative to the fluid.
The dimensional form of the equation is expressed as MLT-2, where M is mass, L is length, and T is time. Stokes’ law was first derived by Irish physicist Sir George Stokes as a result of his 1851 paper on the effect of the viscous flow caused by fluid drag on the motion of a sphere in a fluid.
When can Stokes law be applied?
Stokes law can be applied to relatively small particles, usually smaller than 1 micrometer in diameter, settling under gravity in a fluid medium. This law is most often used to predict the settling velocity of particles in a variety of situations, including sub-aqueous sedimentation, dust settling in the atmosphere, and particle motion in industrial pipelines and vessels.
It can also be used to calculate the frictional drag force and terminal velocity on a particle moving through an ambient fluid, or to calculate hydrometry, the study of suspended sediment concentration in a body of water.
In addition, Stokes law has applications in the field of robotics, particularly for calculating the velocities of self-propelled robots. Finally, it is also used in the development of nanoscale diagnostic and therapeutic devices, such as microfluidic devices, which rely on the precise control of liquid flow, thus allowing them to work effectively at the nanoscale.
What is the formula for viscous force?
The formula for viscous force is equal to the product of the dynamic viscosity and the velocity gradients perpendicular to each other. The mathematical equation for this is F = η * (∂u/∂y + ∂v/∂x). The Greek symbol η means the dynamic viscosity.
Viscous force is the frictional force resisting and opposing the relative motion of layers of a fluid that are moving against each other. It is significantly affected by the distance between the layers,the area over which the force acts, and the dynamic viscosity of the fluid.
The velocity gradients, ∂u/∂y and ∂v/∂x, represent the change in velocity with respect to the distance in the directions perpendicular to each other.
In simpler terms, the formula for viscous force is equal to the dynamic viscosity of a fluid multiplied by the velocity gradients in both directions (I. e. horizontal and vertical). This formula can significantly helpful for science and engineering applications.
What is dimensional formula of viscosity?
The dimensional formula of viscosity is MLT^-1. Viscosity is the measure of a fluid’s resistance to flow, and is denoted by the Greek letter η (eta). It is also sometimes referred to as a “fluid friction” or “fluidity” and has units of Poise (P), centiPoise (cP), or Pascal seconds (Pa s).
The dimensional formula of viscosity is derived by multiplying the base quantities mass (M), length (L) and time (T) together. Thus, the dimensional formula of viscosity is written as [M L T^-1].
What is Stokes law in chemical engineering?
Stokes law in chemical engineering is a law that suggests the terminal settling velocity of a small spherical particle in a viscous fluid is proportional to the square of its diameter and the square root of its density divided by the dynamic viscosity of the fluid.
It was proposed by the Irish Physicist, Sir George Stokes and first published in 1851. This law states that the drag force acting on a particle is proportional to the particle’s settling velocity, and is given by Fd = 6πρvrη, where Fd is the drag force in either Newton or dynes, ρ is the fluid mass density, v is the particle’s settling velocity, r is the particle’s radius, and η is the dynamic viscosity of the fluid.
This law applies to small particles with diameters less than 2 mm, which include suspensions of minerals, proteins, and other colloiids in aqueous solution. This law is also used to explain the sedimentation of large molecules, such as proteins, DNA, and viruses.
The Stokes law is a useful tool in the field of chemical engineering, as it can be used to understand the behavior of different types of particles in different types of fluids.
What is terminal velocity Class 11?
Terminal velocity is the maximum speed at which a falling object can reach when the downward force of gravity counteracts the upward force of drag created by the body’s motion against a medium like air.
In the context of Class 11, terminal velocity is the maximum speed achieved by a freely falling body when acceleration due to gravity is the only force acting upon it. Terminal velocity can vary greatly depending on the shape and mass of the object.
It is also affected by air resistance, which increases with the surface area of the object. On Earth, a typical terminal velocity for a human skydiver in a belly-to-earth (ft2) position is around 120 mph, while a smaller object like a golf ball is only around 80 mph.
Terminal velocity can also be experienced in water, where a person in a feet-first position can reach a maximum speed of around 200 mph.
What is the study of the properties of fluids in motion is called?
The study of the properties of fluids in motion is called fluid dynamics. This is a branch of physics that deals with the study of how fluids move and how different forces affect them. It is a field of science that includes both experimental and theoretical studies.
Fluid dynamics focuses on analyzing the effects of pressure, velocity, density, temperature, and viscosity on the motion of fluids. It has applications in many areas, such as aerodynamics, meteorology, oceanography, astrophysics, biomechanics, and chemical engineering.
Fluid dynamics research can provide insight into such diverse topics as aircraft and rockets’ responding to lift and drag forces, thermal convection’s influence on climate, and aquatic animal’s optimizing their swimming performance.
How do I apply for Stokes law?
To apply for Stokes law, you need to have a foundational understanding of fluid mechanics and the law itself. Stokes law applies to spheres and other particles suspended in fluid flow, and relates particle size, shape, and the viscosity and density of the fluid to the efficient rate of sedimentation.
To apply this law, you need to begin by collecting data on the size, shape, and properties of the fluid flow, as well as the particles to be studied.
Once you have the data, you need to apply the equations of Stokes law to the data to calculate the rate of sedimentation. To do this, you will need to use a calculator or an online calculator to simplify the equations and input the values of the parameters.
If you do not know the properties of the particular particles or the properties of the fluid, you will need to perform experiments to gather the necessary data before applying Stokes law.
Once the equations of Stokes law are applied to the data, you can compare the results of the equations to the expected values to determine the accuracy of the law or to see how the properties of the particles and fluid affect the sedimentation rate.
Additionally, you can use Stokes law to predict the rate at which the particles may settle and sediment in a given fluid situation.
When applying Stokes law, it is important to keep in mind the assumptions and the limitations of the law itself. Those looking to apply Stokes law need to have a comprehensive understanding of the parameters used in the equation in order to gain the most accurate results for their particular analysis.
What is Stokes law and how is it used in soil science?
Stokes Law is used in soil science to calculate the settling velocity of a particle in a fluid. It states that the force required to move a particle suspended in a fluid is directly proportional to the viscosity of the fluid, the density of the particle, and the diameter of the particle, and inversely proportional to the density of the fluid.
This can be useful in calculations related to soil erosion and deposition, which are important parts of soil science. For example, if the size of the particles in a soil sample are measured, their density can be estimated, and then the rate of erosion and deposition can be calculated by using the calculated removing velocity.
Stokes Law can also be used to measure the size of particles when the velocity of settling is known. This is especially useful when studying various types of soils in a laboratory setting.
How does Stokes law calculate time?
Stokes law does not calculate time directly. Instead, it is used to calculate the drag force that is felt by a spherical object immersed in a fluid. This information can then be used to calculate the time it takes for an object to fall a certain distance.
The equation for Stokes law states that the force of drag, Fd, acting on a spherical object with a diameter, d, that is moving through a fluid at a speed, v, is given by:
Fd = 6πµdv
Where µ is the dynamic viscosity of the fluid.
To determine the time it takes an object to fall a certain distance, Fd must be related to acceleration (gravity acts as the acceleration). To do this, the equation Fd = ma (force equals mass times acceleration) is used, where m is the mass of the object.
By rearranging the equation and substituting in the Stokes law equation, it is possible to determine the final speed of the object.
To determine the time of fall, the equation distance = velocity x time is used. Knowing the initial velocity of the object and the final velocity (determined using the equation mentioned above) it is possible to calculate the time.
In summary, although Stokes law does not calculate time directly, it is possible to use the information it provides to calculate the time of an object’s fall.
On what factors does Stokes law depend?
Stokes’ law, also known as Stokes-Einstein equation, is a mathematical relationship between the terminal velocity of a sphere and the size, density, and viscosity of the fluid in which it is moving. The law, developed by English physicist George Stokes in 1851, explains the behavior of small particles suspended in a liquid or gas.
The basic form of Stokes’ law is as follows:
V = 3ηr / 6π∆p
Where V is the settling velocity, η is the viscosity of the fluid, r is the radius of the particle, and ∆p is the difference in pressure between the top and bottom of the particle.
Stokes’ law, therefore, depends on several factors, including the viscosity of the fluid, the size and density of the particle, and the difference in pressure between the top and bottom of the particle.
If any of these factors change, the terminal velocity will be affected. For example, a larger or denser particle will settle more quickly, whereas a lower viscosity fluid will cause the particle to settle more slowly than in a higher viscosity fluid.
The difference in pressure between the top and bottom of the particle will also affect the settling velocity. If there is no pressure difference, the particle will not move.
How do you find settling velocity using Stokes law?
Settling velocity can be found using Stokes law, which states that the terminal velocity of a sphere falling in a viscous fluid is equal to the force of gravity on the sphere divided by the drag force created by the viscosity of the fluid.
More specifically, the equation is:
V = (2*g*r*(ρs – ρf))/(9μ)
where V is the settling velocity, g is the gravitational acceleration, r is the radius of the sphere, ρs and ρf are the densities of the sphere and the fluid respectively, and µ is the viscosity of the fluid.
By plugging in the necessary values into the equation, one can find the settling velocity. Additionally, if the velocities of particles above a certain size become too close to the velocity of the fluid, the separating forces become too weak, allowing the particles to remain suspended, hence the term “stokes settling velocity.
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